Quantum‐TreeSoft Set and Quantum‐ForestSoft Set

Abstract

Fuzzy Sets [1, 2], Neutrosophic Sets [3], and Plithogenic Sets [4] address uncertainty and have diverse ap- plications. The Soft Set framework associates each parameter with subsets of a universe, allowing flexible approximations [5]. Its extensions include Fuzzy Soft Sets [6], Neutrosophic Soft Sets [7], HyperSoft and SuperHyperSoft Sets [8, 9], TreeSoft Sets [10], ForestSoft Sets [11], and GraphicSoft Sets [12]. A TreeSoft Set organizes parameters hierarchically, while a ForestSoft Set unites multiple TreeSoft Set mappings. A Quantum-Soft Set assigns each attribute to a normalized quantum superposition [13]. In this paper, we introduce Quantum TreeSoft Sets and Quantum ForestSoft Sets, extending the Quantum-Soft Set through hierarchical and forest structures. These constructions aim to advance research at the intersection of Quantum Theory and Soft Set Theory.